Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-y &= 4 \\ -6x+y &= 6\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {6x+6}$ Substitute this expression for $y$ in the first equation. $-2x-({6x + 6}) = 4$ $-2x - 6x - 6 = 4$ Simplify by combining terms, then solve for $x$ $-8x - 6 = 4$ $-8x = 10$ $x = -\dfrac{5}{4}$ Substitute $-\dfrac{5}{4}$ for $x$ back into the top equation. $-2( -\dfrac{5}{4})-y = 4$ $\dfrac{5}{2}-y = 4$ $-y = \dfrac{3}{2}$ $y = -\dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{5}{4}, \enspace y = -\dfrac{3}{2}$.